GTI-space: the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI-space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given.     

Calculation of retention indices by molecular topology. Chlorinated benzenes

A comparative study was undertaken to test the ability of several different topological indices to predict the retention indices of chlorinated benzenes on polar and non-polar stationary phases using both correlation coefficients and correctly predicted elution sequences as criteria of fit. The test was performed on three topological indices: connectivity indices, Wiener numbers, and Balaban indices. The regression analyses showed that the molecular connectivity model predicted the retention indices of chlorinated benzenes more successfully than either Wiener numbers or Balaban indices. The results also demonstrated that the major structural property controlling chromatographic behavior was the size of the chlorinated benzene. In addition, the use of the new non-empirical heteroatom parameterization scheme in the calculation of Wiener numbers and Balaban indices was successfully tested for the first time.     

Generalized Hosoya polynomials of hexagonal chains

Similar to the well-known Wiener index, Eu et al. [Int. J. Quantum Chem. 106 (2006) 423–435] introduced three families of topological indices including Schultz index and modified Schultz index, called generalized Wiener indices, and gave the similar formulae of generalized Wiener indices of hexagonal chains. They also mentioned three families of graph polynomials in x, called generalized Hosoya polynomials in contrast to the (standard) Hosoya polynomial, such that their first derivatives at x = 1 are equal to generalized Wiener indices. In this note we gave explicit analytical expressions for generalized Hosoya polynomials of hexagonal chains.     

直链烷烃取代衍生物Wiener指数的简便计算方法

根据直链烷烃衍生物分子拓扑结构的特点,将直链烷烃衍生物拆分为由直链单元和取代基团几个部分构成,再根据每部分的拓扑结构特点给出相应的计算公式.从而提出了一个计算直链烷烃衍生物Wiener指数的简便方法,达到简化计算的目的.该方法简化了传统Wiener指数的计算方法,使Wiener指数的计算具有效率高、不易出错等优点,便于Wiener指数计算程序化,从而提高了Wiener指数的实用性.     

Generalized Wiener indices in hexagonal chains

The Wiener index, or the Wiener number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener index for trees, and Ivan Gutman proposed a modification of the Schultz index with similar properties. We deduce a similar relationship between these three indices for catacondensed benzenoid hydrocarbons (graphs formed of concatenated hexagons, or hexagonal chains, or sometimes acenes). Indeed, we may define three families of generalized Wiener indices, which include the Schultz and Modified Schultz indices as special cases, such that similar explicit formulae for all generalized Wiener indices hold on hexagonal chains. We accomplish this by first giving a more refined proof of the formula for the standard Wiener index of a hexagonal chain, then extending it to the generalized Wiener indices via the notion of partial Wiener indices. Finally, we discuss possible extensions of the result. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Integration of Graph Theory and Quantum Chemistry for Structure-Activity Relationships

Abstract

The objective of this article is to outline both graph-theoretically based and quantum chemically based structural indices of potential use in quantitative structure activity correlations. We consider graph-theoretical indices such as the connectivity index, topological index, Wiener index and molecular ID indices. Several structural and geometry-dependent indices can be derived from semiempirical and ab initio quantum calculations based on the charge densities, overlap matrices, frontier orbitals, molecular hardness, free valence, density matrices, quantum spectral difference indices, quantum spectral indices and bond matrices. Finally, the use of electrostatic potentials and charge densities for the prediction of reactive sites will be discussed.     

The overall Wiener index--a new tool for characterization of molecular topology.

Recently, the concept of overall connectivity of a graph G, TC(G), was introduced as the sum of vertex degrees of all subgraphs of G. The approach of more detailed characterization of molecular topology by accounting for all substructures is extended here to the concept of overall distance OW(G) of a graph G, defined as the sum of distances in all subgraphs of G, as well as the sum of eth-order terms, (e)OW(G), with e being the number of edges in the subgraph. Analytical expressions are presented for OW(G) of several basic classes of graphs. The overall distance is analyzed as a measure of topological complexity in acyclic and cyclic structures. The potential usefulness of the components of this generalized Wiener index in QSPR/QSAR is evaluated by its correlation with a number of properties of C3-C8 alkanes and by a favorable comparison with models based on molecular connectivity indices.     

Molecular modeling of wine polyphenols

Due to wide range of health effects of wine polyphenols, it is important to investigate the relationship between their structure and physical properties (quantitative structure–property relationship, QSPR). We have investigated linear, nonlinear (polynomial), and multiple linear relationships between given topological indices and molecular properties of main pharmacological active components of wine, such as molecular weight (MW), van der Waals volume (Vw), molar refractivity (MR), polar molecular surface area (PSA) and lipophilicity (log P). Partition coefficient (log P) was calculated using three different computer program (CLOGP, ALOGPS and MLOGP). The best models were achieved using the MLOGP program. Topological indices used for correlation analysis include: the Wiener index, W(G); connectivity indices, χ(G); the Balaban index, J(G); information-theoretic index, I(G); and the Schultz index, MTI(G). QSPR was performed on the set of 19 polyphenols and, particularly, on the group of phenolic acids, and on the group of flavonoids with resveratrol. The connectivity index has been successfully used for describing almost all parameters. Significant correlations were achieved between the Wiener index and van der Waals volume, as well as molecular weight.